The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.

1.
R.
Benzi
,
G.
Parisi
,
A.
Sutera
, and
A.
Vulpiani
,
Tellus
34
,
10
(
1982
);
R.
Benzi
,
A.
Sutera
, and
A.
Vulpiani
,
J. Phys. A
14
,
L453
(
1981
).
2.
B.
McNamara
and
K.
Wiesenfeld
,
Phys. Rev. A
39
,
4854
(
1988
);
L.
Gammaitoni
,
F.
Marchesoni
,
E.
Menichella-Saetta
, and
S.
Santucci
,
Phys. Rev. Lett.
62
,
349
(
1989
).
[PubMed]
3.
B.
McNamara
,
K.
Wiesenfeld
, and
R.
Roy
,
Phys. Rev. Lett.
60
,
2626
(
1988
).
4.
L.
Gammaitoni
,
P.
Hänggi
,
P.
Jung
, and
F.
Marchesoni
,
Rev. Mod. Phys.
70
,
223
(
1998
).
5.
F.
Julicher
,
A.
Ajdari
, and
J.
Prost
,
Rev. Mod. Phys.
69
,
1269
(
1997
).
6.
M. O.
Magnasco
,
Phys. Rev. Lett.
71
,
1477
(
1993
);
[PubMed]
C. R.
Doering
,
W.
Horsthemke
, and
J.
Riordan
,
Phys. Rev. Lett.
72
,
2984
(
1994
).
[PubMed]
7.
H.
Linke
,
T. E.
Humphrey
,
A.
Lfgren
,
A. O.
Sushkov
,
R.
Newbury
,
R. P.
Taylor
, and
P.
Omling
,
Science
286
,
2314
(
1999
);
[PubMed]
L. Q.
Zhou
,
X.
Jia
, and
Q.
Ouyang
,
Phys. Rev. Lett.
88
,
138301
(
2002
).
[PubMed]
8.
J.
Garcia-Ojalvo
,
A.
Hernandez-Machado
, and
J. M.
Sancho
,
Phys. Rev. Lett.
71
,
1542
(
1993
).
9.
A.
Becker
and
L.
Kramer
,
Phys. Rev. Lett.
73
,
955
(
1994
);
[PubMed]
A.
Becker
and
L.
Kramer
,
Physica D
90
,
408
(
1995
).
10.
J. M. R.
Parrondo
,
C.
Van den Broeck
,
J.
Buceta
, and
F. J.
de la Rubia
,
Physica A
224
,
153
(
1996
).
11.
A. A.
Zaikin
and
L.
Schimansky-Geier
,
Phys. Rev. E
58
,
4355
(
1998
).
12.
J.
Buceta
,
M.
Ibanes
,
J. M.
Sancho
, and
K.
Lindenberg
,
Phys. Rev. E
67
,
021113
(
2003
).
13.
S.
Dutta
,
S. S.
Riaz
, and
D. S.
Ray
,
Phys. Rev. E
71
,
036216
(
2005
).
14.
C. R.
Doering
and
J. C.
Gadoua
,
Phys. Rev. Lett.
69
,
2318
(
1992
).
15.
M.
Bier
and
R. D.
Astumian
,
Phys. Rev. Lett.
71
,
1649
(
1993
);
[PubMed]
U.
Zürcher
and
C. R.
Doering
,
Phys. Rev. E
47
,
3862
(
1993
).
16.
C.
Van den Broeck
,
Phys. Rev. E
47
,
4579
(
1994
).
17.
J. J.
Brey
and
J.
Casado-Pascual
,
Phys. Rev. E
50
,
116
(
1994
);
O.
Flomenbom
and
J.
Klafter
,
Phys. Rev. E
69
,
051109
(
2004
).
18.
T. D.
Shepherd
and
R.
Hernandez
,
J. Chem. Phys.
115
,
2430
(
2001
);
A. M.
Berezhkovskii
,
A.
Szabo
,
G. H.
Weiss
, and
H.
Zhou
,
J. Chem. Phys.
111
,
9952
(
1999
).
19.
M.
Boquñá
,
J. M.
Porrá
,
J.
Masoliver
, and
K.
Lindenberg
,
Phys. Rev. E
57
,
3990
(
1998
).
20.
M.
Marchi
,
F.
Marchesoni
,
L.
Gammaitoni
,
E.
Menichella-Saetta
, and
S.
Santucci
,
Phys. Rev. E
54
,
3479
(
1995
).
Y.
Jia
and
J. R.
Li
,
Phys. Rev. E
53
,
5786
(
1996
);
X.
Luo
and
S.
Zhu
,
Phys. Rev. E
67
,
021104
(
2003
).
22.
R. N.
Mantegna
and
B.
Spagnolo
,
Phys. Rev. Lett.
84
,
3025
(
2000
).
23.
J.
Maddox
,
Nature (London)
359
,
771
(
1992
).
24.
J.
Wang
and
P.
Wolynes
,
Chem. Phys.
180
,
141
(
1994
).
25.
J. M.
Martinis
,
M. H.
Devoret
, and
J.
Clarke
,
Phys. Rev. Lett.
55
,
1543
(
1985
).
26.
R. L.
Stratonovich
,
Topics in the Theory of Random Noise
(
Gordon and Breach
, New York,
1963
), Vol.
1
;
K.
Lindenberg
and
B. J.
West
,
J. Stat. Phys.
42
,
201
(
1986
);
J.
Masoliver
,
B. J.
West
, and
K.
Lindenberg
,
Phys. Rev. A
35
,
3086
(
1987
);
D.
Mei
,
G.
Xie
,
L.
Cao
, and
D.
Wu
,
Phys. Rev. E
59
,
3880
(
1999
).
27.
H.
Mori
,
Prog. Theor. Phys.
33
,
423
(
1965
);
H.
Mori
and
H.
Fujisaka
,
Prog. Theor. Phys.
49
,
764
(
1973
);
M.
Tokuyama
and
H.
Mori
,
Prog. Theor. Phys.
55
,
411
(
1976
);
M.
Tokuyama
and
H.
Mori
,
Prog. Theor. Phys.
56
,
1073
(
1976
).
28.
L. S.
Garcia-Colin
and
J. L.
Del Rio
,
J. Stat. Phys.
16
,
235
(
1977
);
L. S.
Garcia-Colin
and
J. L.
Del Rio
,
Physica A
96
,
606
(
1979
);
H.
Furukawa
,
Prog. Theor. Phys.
62
,
70
(
1979
).
29.
K.
Ogan
, in
Advances in Magnetic Resonance
, edited by
J. S.
Waugh
(
Academic
, New York,
1974
), Vol.
7
.
30.
R.
Zwanzig
,
J. Stat. Phys.
9
,
215
(
1973
).
31.
D.
Banerjee
,
B. C.
Bag
,
S. K.
Banik
, and
D. S.
Ray
,
Phys. Rev. E
65
,
021109
(
2002
).
32.
D.
Banerjee
,
B. C.
Bag
,
S. K.
Banik
, and
D. S.
Ray
,
J. Chem. Phys.
120
,
8960
(
2004
).
33.
P. K.
Ghosh
,
D.
Barik
, and
D. S.
Ray
,
Phys. Rev. E
71
,
041107
(
2005
).
34.
P. K.
Ghosh
,
D.
Barik
, and
D. S.
Ray
,
Phys. Lett. A
342
,
12
(
2005
).
35.
D.
Barik
and
D. S.
Ray
,
J. Stat. Phys.
120
,
339
(
2005
).
36.
A.
Mielke
,
Ann. Phys.
4
,
476
(
1995
);
J. M.
Sancho
,
Phys. Rev. A
31
, R
3523
(
1985
);
J. M.
Gutierrez
,
A.
Iglesias
, and
M. A.
Rodriguez
,
Phys. Rev. E
48
,
2507
(
1993
).
37.
38.
M.
Hillery
,
R. F.
O’Connell
,
M. O.
Scully
, and
E. P.
Wigner
,
Phys. Rep.
106
,
121
(
1984
).
39.
W. H.
Louisell
,
Quantum Statistical Properties of Radiation
(
Wiley
, New York,
1990
), p.
426
.
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